Setting a limit could help, but depending on the limit, it might turn into a fake-cheat cheating terminal instead of full on cheat. actually, it might feel like offline rewards. I'm not sure how to balance a cheat system without making it not a cheat but if you could somehow make it work I would love to see how it turns out in the end, especially since I love puzzles and would love to figure out the 20 achievement/criminal record tied to the terminal.
Also, if you already have some ideas for Analysis, then great! I'll look forward to what you got planned for it :D